You probably won't get much binding due to the amine content of the buffer, there'll be just too many. Use an MES or PBS instead. Nucleic acids will be better at RT for this reaction.
Yes tris is likely to be a problem. Just desalt the sample into a more appropriate buffer. I would personally use a buffer of much higher pH than is achievable with MES or PBS, as the resulting schiff base is more stable in alkaline buffer. Carbonate can be used for example. You may also need to stabilize the bond by reduction.